How do you find the equation of the tangent line and normal line to the curve #y = (5+6x)^2# at the point (-4,361)?
1) Equation of Tangent
The tangent is a line so it has the form of a line:
Also the gradient,
At the point
Putting the point
hence equation of tangent is
Equation of normal
The equation of normal is also a line of the same form as the tangent.
The only difference is at the level of the gradient.
We can deduce the gradient of the normal from the fact that the normal is a line perpendicular to the tangent
This implies the product of their gradients is
Hence equation of normal is